### From Outcrop Geology to Seismic… and Back!

When I started studying geophysics, the teacher introducing seismic arrived one day with colored pencils and a bunch of paper rolls; we then laid these over a few tables and discovered our first seismic sections. I was not impressed at the time and thought that interpreting seismic was not going to be for me! Fellow students thought it was fun, while I wondered how on earth one could trust these colored lines we drew, viewing the sections sidewayson to better appreciate continuity. Though PCs at the time were barely available for students, a very few of us got really enthralled, and had fun testing Fortran-like codes on our one computer and discovering modeling and imaging (Claerbout, 1985).

This student experience colored my career, as I realized I enjoyed modeling seismic in various ways, though I stayed away from interpretation. Thanks to working on imaging with colleagues in other fields as a young researcher in the early ’90s, I stumbled across the concept of Point-Spread Function (PSF; imaging response of a point scatterer), a well-known key feature of any imaging system, and adapted it for seismic (Lecomte and Gelius, 1998). Using raybased approaches to compute PSF, we applied the function to simulate seismic images by convolution.

But, as long as I was making my own – simplistic – geomodels, the produced seismic images remained…simplistic. However, in 2014 I joined forces with a geologist in need of seismic modeling for fold models and an expert in digital geoscience making virtual outcrop models (VOM) and software. We opened the way for fun and fast – yet realistic enough – targetoriented seismic modeling of possibly complex/detailed geological models. In recent years this has proved to be in high demand, becoming the ‘cherry on the cake’ for various young geoscientists spending a huge amount of time collecting field data or making advanced geomodels; they are finally able to see how it looks on seismic (see reference list for examples). Additionally, for education and industry training, we can now better teach and illustrate seismic interpretation, using hands-on cases where modeling relates both geology and seismic (Figure 1).

#### Do Convolution Modeling…

When teaching seismic interpretation, students always get the classic explanation of the seismic trace resulting from a convolution between a reflectivity log and a wavelet (e.g., Simm and Bacon, 2014), a necessary step towards introducing vertical resolution issues. Students can then see how a high-frequency wavelet better matches the detailed input log rather than a lower frequency one (see Figure 2). Though the wavelet automatically applies a smoothing to the dense log, we often upscale the latter due to technical constraints; for example, to reduce the number of parameters in seismic modeling/inversion due to computing costs (but keep the details if you can!). Then comes the quarter-of-a-wavelength (λ/4) rule of thumb for vertical resolution or tuning thickness. After that, we mention the Fresnel Zone for the lateral resolution issue (cf. Sheriff, 1977), but books often state that this is highly reduced by migration (cf. Lindsey, 1989), yielding a lateral resolution of λ/2 with modern 3D seismic and is therefore not a problem.

Note that, although vertical resolution issues are still discussed at length and wedge models re-created repeatedly, nobody seems to bother about a lateral resolution that is at least twice as bad as the vertical one.

Thereafter, students are made aware of detectability issues (a combination of size and reflection strength) and told that we can theoretically detect thicknesses down to λ/20 – λ/30. Finally, we add that not all structures will be seen by seismic due to illumination issues; the steeper reflectors, for instance, are seldom imaged even if they have proper contrasts.

But these are all rules of thumb and generalities, based on such things as specific wavelets and using simple models. Students then start to work with modern 3D seismic, with spectacular features like fluvial systems enhanced by attributes/color plays, using the industry-standard software they all want to learn to get a job, and these potential seismic pitfalls are long forgotten. The best way is to let students model for themselves, in a learning-by-doing and visual approach, with interactive tools (gaming-like!) designed for the digital generation to gain insight through modeling.

#### … But Not Only Repeated 1D!

As teachers, we need to catch our students’ attention, and I favor ‘fun’ models like those illustrated here, as they stick in the mind better. All the figures have animated versions in this online article, in order to help people better appreciate not only why they should model, but also to help them stop thinking of 1D convolution and instead do a PSF-based one. These examples also encourage students to bear in mind lateral resolution and its relation to illumination, and to consider the small details whenever possible, even in 3D.

Basically, instead of convolving a reflectivity model trace-by-trace with a 1D operator (wavelet), wrongly calling that a 2-3D convolution, a PSF-based approach takes 2-3D models at once and applies 2-3D PSFs to it (e.g. Lecomte et al., 2003; 2015). The illustrations given here are targetoriented and apply a single PSF per image, designed with just a few key parameters for the sake of simplicity and efficiency, but the concept extends to spatially-varying PSFs estimated for given survey geometries and velocity models (e.g. Jensen et al., 2018). Each example is only briefly discussed and readers are encouraged to make their own analyses. Note that the PSF-based approach used here simulates prestack depth-migrated seismic and thus allows direct comparison to actual geology in outcrop.

#### My Favorite ‘Owly’ Model

Animation of "Figure 3: The 'Owly' Model".
As my university’s logo is a good mix of patterns and thicknesses, it can be used as a (fake) 0˚ incidence reflectivity (R0) input model, the original pixel size upscaled to 1x1m2 to reflect seismic sizes (Figure 3a). Utilizing a 20-Hz wavelet and an average velocity of 2 km/s, three seismic-like versions of the logo can be generated: 1D-convolution along vertical lines (3b) and two PSF-based convolutions with (3c) perfect illumination (λ/4 resolution in all directions) and (3d) standard limited illumination (λ/2 lateral resolution with dips steeper than ~45˚ not illuminated). The corresponding PSFs are superimposed in the lower right corner of each image and scaled.

If students first try to guess the original model from (3d), i.e., the most seismic-like version, they fail. When they see (3b) , i.e., 1D-modeled, they identify the logo but this is not a realistic image, showing also some artificial thinning of the steep parts. The illumination needs indeed to be perfect (3c) – difficult to achieve in reality! – for the logo to be identified.

#### The Man on the Outcrop

Animation of "Figure 4: The man on the outcrop. Original picture courtesy of M. Bentley (Ringrose and Bentley, 2015)."
Figure 4 shows modeling of an upscaled fault-zone outcrop picture with a man as our fun target and with the same modeling options as above. The top background photo of a man and an extensional fault network is used as input by converting a grey version of the image into Vp values (ranging from 2–3 km/s), Vs and density being given as simple functions of Vp. The original pixel size is upscaled to 1x1m2 to reflect seismic sizes, the man on the original picture thus turning into a ‘target feature’ of about 100x200m2. After extracting the 0˚ incidence reflectivity R0 (see enlarged zone around the target to the left of the man), a 20-Hz wavelet and an average velocity of 2.5 km/s are used to generate three seismic-like versions of the outcrop: (4a) 1D-convolution along vertical lines; 2D PSF-based convolution with either perfect illumination (4b) or limited (45˚ maximum reflector dip) illumination (4c), the latter yielding the background seismic in the lower half of the figure. The corresponding and scaled PSFs are superimposed at the top of the figure, while the enlarged target is plotted at the bottom. R0 and seismic (4c) are also superimposed on the right of the man.

#### The Fault Zone for Interpretation

Animation of "Figure 5: An upscaled fault zone image can be used for classroom interpretation."
Another upscaled fault zone image (Figure 5) is used for interpretation in class. A small-scale lacquer peel (5a) from a Tertiary sand-pit is the input model, following a similar procedure to the examples above. Figure 5b is the seismic upscaled R0 model with a 1x1m2 pixel size. The remaining sections are modeled with a 20-Hz wavelet and 2 km/s average velocity: (5c) is 1D convolution; 2D PSFbased convolutions are shown in (5d) with perfect illumination, in (5e) with up to 40˚ and in (5f) up to 10˚ maximum reflector dip illuminations. The corresponding PSFs are superimposed in the lower right corner of each section. Students are given figure 5e with a fake well and a few horizon markers and usually successfully map the near-vertical (left) fault, but the right (~55˚dip) fault is less easily identified due to lack of illumination and lateral smearing, while the near-flat reverse fault in the middle is seldom caught. If the illumination is very bad (e.g. below salt or thin high-velocity layers), as in (5f), an extreme lateral smearing is induced.

#### Paleokarst Reservoir

Animation of "Figure 6: A synthetic 3D paleokarst reservoir illustrates the interplay of vertical and lateral resolution".
The synthetic 3D paleokarst reservoir model of a cave system imbedded in a fractured network (Figure 6) illustrates the interplay of vertical and lateral resolution (Furnée, 2015; Johansen, 2018). The top row shows horizontal slices (XY: 600x650m^{2}), while the bottom row shows vertical cross-sections (XZ: 600x135m^{2}). The cell size is 5x5x2.5m^{3}, each seismic modeling taking 15s total running time on a standard laptop, including reflectivity calculation. The reflectivity R0 input model (6a) shows the thin, elongated cave pattern; 1D convolution (6b) shows the impact of the vertical resolution alone, inducing some lateral smearing on XY by ghosting the structures above and below, especially at the area circled, while XZ keep the lateral gaps of the reflectivity. By modeling a more realistic resolution pattern with 3D PSF-based convolution (6c) (45˚maximum reflectordip illumination) the cave is, like seismic, blurred in all directions. All plots are pixelated (without any auto smoothing) to better emphasize the 1-pixel lateral ‘resolution’ of the 1D convolution.

#### Avoiding Pitfalls

These education-related modeling examples are solely intended to catch the eye of students so that they do not forget seismic pitfalls when later playing with advanced, often black-box, software, where they can be ‘blinded’ by the beauty of 3D seismic. However, it would be better for them to fully interact with input (detailed) geology and properly modeled (not 1D) seismics, through efficient, integrated, flexible, and visual workflows. Ideally, all migrated seismic volumes should be handed over with their PSF characteristics to allow such modeling-while-interpreting exercises. Furthermore, PSF-based convolution is ideal for any machine-learning processes in interpretation, as such systems need training.

*References:*

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